{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lesson_9

# Lesson_9 - 'n1 ilxbhpi`e il`ivpxtic oeayg(104010 9 lebxz...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 9 lebxz `xity qixi` :dkixr oxia xnr ,cwy inrp x"c ,ipinipa a`ei 'text :ddbd uixw di`n :dqtcd xeliih gezit :dxcbd aiaq f ( x ) ly n xcqn xeliih mepilet f` x-a (zegtl) minrt n dxifb f ( x ) m` :`ed x T n ( x ) = f ( x ) + f ( x )( x- x ) + f 00 ( x ) 2! ( x- x ) 2 + ... + f ( n ) ( x ) n ! ( x- x ) n :zxvewn daizka ,e` T n ( x ) = n X k =0 f ( k ) ( x ) k ! ( x- x ) k . f ( x ) ly n xcqn oxelwn mepilet mb `xwp xeliih mepilet x = 0 xy`k :zexrd milawn n xcq cr eizexfbpe `edy n-l deey e` dphw dlrnn cigid mepiletd `ed T n ( x ) .1 :xnelk ,i- n-d xcqd cr dizexfbpe f milawny mikxrd mze` z` x dcewpa , ≤ k ≤ n ,T ( k ) n ( x ) = f ( k ) ( x ) yeniya oeirxd . f ( x ) ly sxbl aexw T n ( x ) ly sxbd x ly daiaqae T n ( x ) = f ( x ) .2 .lcbi n-y lkk xtzyi aexiwdy mieewn ep`y `ed xeliih mepileta 1 :`nbec : f ( x ) = ln(1- x ) ly n xcqn oxelwn mepilet aeyig (`) f ( x ) = ln(1- x ) f (0) = 0 f ( x ) =- 1 1- x f (0) =- 1 f 00 ( x ) =- 1 (1- x ) 2 f 00 (0) =- 1 f (3) ( x ) =- 2(1- x )- 3 f (3) (0) =- 2 f (4) ( x ) =- 2 · 3(1- x )- 4 f (4) (0) =- 2 · 3 =- 3! . . . . . . f ( k ) ( x ) =- ( k- 1) !(1- x )- k f ( k ) (0) =- ( k- 1) ! T n ( x ) = n X k =0 f ( k ) (0) x k k ! = n X k =1- ( k- 1)! x k k ! =- n X k =1 x k k :`ed g ( x ) = 1 1- x ly n xcqn oxelwn mepilet (a) T n ( x ) = n X k =0 x k = 1 + x + x 2 + ... + x n .` sirqa aeyigd lr jnzqpe g ( k ) ( x ) =- ( ln(1- x ) ) (...
View Full Document

{[ snackBarMessage ]}